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Multiwin
Topic Author
Posts: 7
Joined: May 17th, 2005, 2:41 pm

### Option on variance swap

HiCan someone explain to me(or send me an article) how to price an option on a variance swap?many thanks

eiriamjh
Posts: 462
Joined: October 22nd, 2002, 8:30 pm

### Option on variance swap

I am afraid this is still an open problemyou might want to look for Roger Lee's presentation on volatility derivatives... but I still don t see clearly what is the hedging strategy behind his approach

exotiq
Posts: 1888
Joined: October 13th, 2003, 3:45 pm

### Option on variance swap

Look up an old article on the topic by Alex Lipton and Dmitry Pugachevsky that uses the Heston model to price it as an integral over a non-central Chi-squared distribution.In my experience, that technique doesn't work that well, but it's important to understand as background. There are other stochastic vol models which give more stable solutions w.r.t the market, so move on to those...

exotiq
Posts: 1888
Joined: October 13th, 2003, 3:45 pm

### Option on variance swap

QuoteOriginally posted by: eiriamjhI am afraid this is still an open problemyou might want to look for Roger Lee's presentation on volatility derivatives... but I still don t see clearly what is the hedging strategy behind his approachFrom what I've seen, Roger Lee and Peter Carr's work focus on options on realized vol variance more than options on implied variance (options to enter into variance swaps).The OTC market doesn't care what problems are open or closed; they were trading options before Black-Scholes, and are happy to make markets (be they ever so wide) in SX5E and NDX variance swaptions for the right price.I have found that using several different stochastic vol models is a good guide for where the price should be, and for the hedges, the forward vega values I get from cliquet models are about as good as any other forward-variance model's...

doublebarrier2000
Posts: 237
Joined: July 14th, 2002, 3:00 am

### Option on variance swap

hiwhen you say "an option on a variance swap" I assume you mean a REALISED variance swap as these are widely traded.you then say "Roger Lee and Peter Carr's work focus on options on realized vol variance more than options on implied variance (options to enter into variance swaps)."I don't recall seeing implied vol swaps. If they exist I would appreciate any info.With regard to options on realised vol/var swaps, I assumeneed to use a model incorporating the vol of vol.

eiriamjh
Posts: 462
Joined: October 22nd, 2002, 8:30 pm

### Option on variance swap

doublebarrier: I believe exotiq is making the distinction between an option to buy realized variance at maturity at a pre-agreed price, and an option to enter into a variance swap at maturity at a pre-agreed strikee.

probably
Posts: 175
Joined: May 18th, 2004, 10:46 pm

### Option on variance swap

I've been working on models for variance swap term structures, in case you are interested http://www.math.tu-berlin.de/~buehler/ (the presentation is better understandable).Such models will allow you to price eithe trade discussed below (let me note that all continuous models with finite representation fit into it, ie also local vol).Also, these models have rougjly appropriate future implied vol dynamics.PS better readable paper upcoming after weekend
Last edited by probably on May 27th, 2005, 10:00 pm, edited 1 time in total.

Multiwin
Topic Author
Posts: 7
Joined: May 17th, 2005, 2:41 pm

### Option on variance swap

Thanks guys!Probably, can you please send me the article you are talking about? on the website you mention there is no link to the paper called "Hedging options on variance". Thanks in advance.

PutorCall
Posts: 166
Joined: November 27th, 2002, 1:45 am

### Option on variance swap

The work by Roger Lee and I is on pricing options on realized variance i.e. terminal quadraticvariation of log price .This is not the same thing as pricing an option on a variance swap.Tell me which of the two topics you are interested in and I can send relevant cites.

Multiwin
Topic Author
Posts: 7
Joined: May 17th, 2005, 2:41 pm

### Option on variance swap

I'm interested by pricing options on variance swaps(and how to hedge them in practice).Many thanks for your help.

QuantSeb
Posts: 17
Joined: October 13th, 2002, 6:56 am

### Option on variance swap

Multiwin,In my opinion, pricing volatility claims cannot be done in the traditional risk-neutral sense, due to the fact that the derivative is written on a non tradeable asset. The right approach is therefore inspired from the utility-based pricing (and hedging) of options. A recent article about the application of this methodology is the context of volatility claims is the one from Hurd & Grasselli "Indifference pricing and hedging in stochastic volatility models". This article contains also a list of references related to the utility-based prices.Best,QuantSeb.

MForde
Posts: 86
Joined: March 30th, 2005, 9:03 am

### Option on variance swap

a variance swap is worth the same as some portfolio of vanillas by standard resultsso an option on a variance swap is just a non-standard compound optionGoodnight sports fans

probably
Posts: 175
Joined: May 18th, 2004, 10:46 pm

### Option on variance swap

Hi Multiwin,the paper you mention is internal (that's why there's no link) but the paper on the same site on consistent variance curves,or better the presentation gives you the model background ... You then get an idea at where we are heading at hereBest
Last edited by probably on May 31st, 2005, 10:00 pm, edited 1 time in total.

probably
Posts: 175
Joined: May 18th, 2004, 10:46 pm

### Option on variance swap

Hi QuantSeb,Why is an option on a variance swap an option on a non-traded asset? Variance swaps are traded,and forward variance swaps are just the difference between two variance swaps-> so you can tradethe underlying of your option (as MForde said it's "just" a compound option).That's why I think you should model directly (under risk-neutrality) the (forward) variance swaps, justas forward rates and if you got the vols somehow close to reality (and all the other smallprint), thenyou should be able to hedge the thing. Intuitively (for me, that is) you want to hedge an option ona variance swap by the forward variance swap itself plus maybe some residual sensitivities(the standard Europeans can be used to infer VolOfVol and Correlation to the underlying of thevariance curve).Best
Last edited by probably on May 31st, 2005, 10:00 pm, edited 1 time in total.

achilles
Posts: 37
Joined: February 13th, 2002, 1:14 am

### Option on variance swap

since variance swaps have become so liquid, why doesnt one just treat the variance swap is the underlying and then go about pricing via BS? will have to look at quotes of variance to get implied vols of the variance swap...